This preview shows page 1. Sign up to view the full content.
Unformatted text preview: andard deviation of price movements is not an adequate measure of the appropriateness of adding oil stocks to a portfolio. 9. 10. The statement is false. If a security has a negative beta, investors would want to hold the asset to reduce the variability of their portfolios. Those assets will have expected returns that are lower than the riskfree rate. To see this, examine the Capital Asset Pricing Model: E(RS) = Rf + β S[E(RM) – Rf] If β S < 0, then the E(RS) < Rf Solutions to Questions and Problems NOTE: All endofchapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem. Basic 1. The portfolio weight of an asset is total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 95($53) + 120($29) = $8,515 The portfolio weight for each stock is: WeightA = 95($53)/$8,515 = .5913 WeightB = 120($29)/$8,515 = .4087 270 2. The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. The total value of the portfolio is: Total value = $1,900 + 2,300 = $4,200 So, the expected return of this portfolio is: E(Rp) = ($1,900/$4,200)(0.10) + ($2,300/$4,200)(0.15) = .1274 or 12.74% 3. The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. So, the expected return of the portfolio is: E(Rp) = .40(.11) + .35(.17) + .25(.14) = .1385 or 13.85% 4. Here we are given the expected return of the portfolio and the expected return of each asset in the portfolio and are asked to find the weight of each asset. We can use the equation for the expected return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1 (100%), the weight of Stock Y must be one minus the weight of Stock X. Mathematically speaking, this means: E(Rp) = .129 = .16wX + .10(1 – wX) We can now solve this equation for the weight of Stock X as: .129 = .16wX + .10 – .10wX .029 = .06wX wX = 0.4833 So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = 0.4833($10,000) = $4,833.33 And the dollar amount invested in Stock Y is: Investment in Y = (1 – 0.4833)($10,000) = $5,166.67 5. The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of the asset is: E(R) = .2(–.09) + .5(.11) + .3(.23) = .1060 or 10.60% 271 6. The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of each stock asset is: E(RA) = .15(.06) + .65(.07) + .20(.11) = .0765 or 7.65% E(RB) = .15(–.2) + .65(.13) + .20(.33) = .1205 or 12.05% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then add all of these up. The result is the variance. So, the variance and standard deviation of each stock are: σ A2 =.15(.06 – .0765)2 + .65(.07 – .0765)2 + .20(.11 – .0765)2 = .00029 σ A = (.00029)1/2 = .0171 or 1.71% σ B2 =.15(–.2 – .1205)2 + .65(.13 – .1205)2 + .20(.33 – .1205)2 = .02424 σ B = (.02424)1/2 = .1557 or 15.57% 7. The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of the stock is: E(RA) = .10(–.045) + .25 (.044) + .45(.12) + .20(.207) = .1019 or 10.19% To calculate the standard deviation, we first need to calculate the variance. To find the variance, we find the squared deviations from the expected return. We then multiply each possible squared deviation by its probability, and then add all of these up. The result is the variance. So, the variance and standard deviation are: σ 2 =.10(–.045 – .1019)2 + .25(.044 – .1019)2 + .45(.12 – .1019)2 + .20(.207 – .1019)2 = .00535 σ = (.00535)1/2 = .0732 or 7.32% 8. The expected return of a portfolio is the sum of the weight of each asset times the expected return of each asset. So, the expected return of the portfolio is: E(Rp) = .15(.08) + .65(.15) + .20(.24) = .1575 or 15.75% If we own this portfolio, we would expect to get a return of 15.75 percent. 272 9. a. To find the expected return of the portfolio, we need to find the return of the portfolio in each state of the economy. This portfolio is a special case since all three assets have the same weight. To find the expected return in an equally weighted portfolio, we can sum the returns of each asset and divide by the number of assets,...
View
Full
Document
This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

Click to edit the document details